As a prediction of GR, GW has been first observed by aLIGO on September 14, 2015 [1]}, and 90 GW events have been reported by the LVK collaboration up to now [2]}, [3]}, [4]}, [5]}, [6]}.
The analysis of GW150914 and all the GWTC events [7]}, [8]}, [9]}, [10]}, [11]} shows that no deviation of GR has been detected with current observations.
However, more sensitive observatories such as ET [12]} and CE [13]} on the Earth, or TianQin [14]} and LISA [15]} in space, will be built in the future.
So the deviation of GR may be observed, or be constraint to a higher level with the data which is more accurate.
Most of the constraint is obtained by model dependent method, which means that we need to calculate the waveform of the sources in GR or in the alternative theory, thus the inaccurate of the waveform model may cause misinterpretation of the observed data.
However, the polarization mode, a intrinsic feature of GW, can be used to test GR in a model independent way.
